This proof is similar to the proof of Lemma J.3 in [1]} so we only give a sketch here. Firstly we have
\(\begin{aligned}[b]\kappa _D(s^{\prime })^2 \ge \min \bigg \lbrace \frac{^T \nabla ^2_{} R^n_{\delta }(\widehat{})}{\Vert \Vert _2^2 } : \in ^{d-1} \backslash \lbrace 0\rbrace , \Vert _{s^{\prime c}}\Vert _1 \le \xi \Vert _{s^{\prime }}\Vert _1\bigg \rbrace .\end{aligned}\) 
